{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## An `A <-> B` reaction \n", "with 1st-order kinetics in both directions, taken to equilibrium,\n", "using a simple, coarse fixed-timestep simulation. \n", "\n", "Afterwards, perform some analysis of the results\n", "\n", "See also the experiment _\"1D/reactions/reaction_1\"_ for a multi-compartment version. \n", "\n", "This experiment gets continued in _\"react_2_b\"_ , with a more sophisticated approach, \n", "involving adaptive variable time steps.\n", "\n", "LAST REVISED: May 6, 2024" ] }, { "cell_type": "code", "execution_count": 1, "id": "1f552123-2456-42fa-9fea-42582e096c0f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "import set_path # Importing this module will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 2, "id": "b0ce3cdd", "metadata": { "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "from src.modules.visualization.plotly_helper import PlotlyHelper\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "83c3cc5f-de21-4f66-9988-2806fbf0666d", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'react_2_a.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging (for the graphics)\n", "log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "code", "execution_count": null, "id": "eed9fe97-872a-44de-93ba-c499a6f1191b", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "# Initialize the System" ] }, { "cell_type": "code", "execution_count": 4, "id": "72b4245c-de4e-480d-a501-3495b7ed8bc4", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1\n" ] } ], "source": [ "# Instantiate the simulator and specify the chemicals\n", "dynamics = ReactionDynamics(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B , with 1st-order kinetics in both directions\n", "dynamics.add_reaction(reactants=[\"A\"], products=[\"B\"], \n", " forward_rate=3., reverse_rate=2.)\n", "\n", "print(\"Number of reactions: \", dynamics.number_of_reactions())" ] }, { "cell_type": "code", "execution_count": 5, "id": "00ea560d-9a49-4041-b119-6de11bfcc7af", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 3 / kR = 2 / delta_G = -1,005.1 / K = 1.5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 6, "id": "cb582868-431c-4022-aa0e-a2f554f80d6c", "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `react_2_a.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions to the HTML log file\n", "dynamics.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "code", "execution_count": 7, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [], "source": [ "# Initial concentrations of all the chemicals, in index order\n", "dynamics.set_conc([10., 50.])" ] }, { "cell_type": "code", "execution_count": 8, "id": "a605dacf-2c67-403e-9aa9-5be25fc9f481", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 10.0\n", " Species 1 (B). Conc: 50.0\n", "Set of chemicals involved in reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 9, "id": "0ff2c242-a15b-456d-ad56-0ba1041c0b4c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.010.050.0Initial state
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.0 50.0 Initial state" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "ab7147fe-712c-4c92-b61f-20ff51675ab8", "metadata": {}, "source": [ "### Test your intuition: \n", "#### given that this reaction operates mostly in the forward direction (kF = 3 , kR = 2 , K = 1.5), \n", "#### do you think that A will be consumed and B will be produced??\n", "We can take a sneak preview at the final equilibrium concentrations without actually running the simulation:" ] }, { "cell_type": "code", "execution_count": 10, "id": "12cac04d-dd61-4646-9339-8b70e22139e8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'A': 24.0, 'B': 36.0}" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.find_equilibrium_conc(rxn_index=0) # This is an EXACT solution" ] }, { "cell_type": "markdown", "id": "ee5b9d1c-3ebe-497a-a0e9-bfb02dcd0693", "metadata": {}, "source": [ "#### The reaction will actually proceed IN REVERSE, because of the large initial concentration of B (which we had set to 50), relative to the small initial concentration of A (10)\n", "Now, let's see the reaction in action!" ] }, { "cell_type": "code", "execution_count": null, "id": "d748df77-1b71-4d16-9e24-212d74a93ff4", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "fc516ca2-e62d-4784-b826-5372ff7f4c75", "metadata": { "tags": [] }, "source": [ "### Run the reaction" ] }, { "cell_type": "code", "execution_count": 11, "id": "50c7e478-ad0e-4aeb-9cea-dfed47cded21", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 total step(s) taken\n" ] } ], "source": [ "# First step of reaction\n", "dynamics.single_compartment_react(initial_step=0.1, n_steps=1, variable_steps=False, \n", " snapshots={\"initial_caption\": \"first reaction step\"})" ] }, { "cell_type": "code", "execution_count": 12, "id": "c9115720-e66e-44f3-bb0a-fabec5b96673", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SYSTEM TIMEABcaption
00.010.050.0Initial state
10.117.043.0first reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.0 50.0 Initial state\n", "1 0.1 17.0 43.0 first reaction step" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "98ec8a03-7a9b-403a-8dcd-d9e19c49d656", "metadata": {}, "source": [ "We can already see the reaction proceeding in reverse..." ] }, { "cell_type": "code", "execution_count": 13, "id": "2502cd11-0df9-4303-8895-98401a1df7b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10 total step(s) taken\n" ] } ], "source": [ "# Numerous more fixed steps\n", "dynamics.single_compartment_react(initial_step=0.1, n_steps=10, variable_steps=False, \n", " snapshots={\"initial_caption\": \"2nd reaction step\",\n", " \"final_caption\": \"last reaction step\"})" ] }, { "cell_type": "code", "execution_count": 14, "id": "80fbaee3-bd6f-4197-9270-23374d46a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.010.00000050.000000Initial state
10.117.00000043.000000first reaction step
20.220.50000039.5000002nd reaction step
30.322.25000037.750000
40.423.12500036.875000
50.523.56250036.437500
60.623.78125036.218750
70.723.89062536.109375
80.823.94531236.054688
90.923.97265636.027344
101.023.98632836.013672
111.123.99316436.006836last reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.000000 50.000000 Initial state\n", "1 0.1 17.000000 43.000000 first reaction step\n", "2 0.2 20.500000 39.500000 2nd reaction step\n", "3 0.3 22.250000 37.750000 \n", "4 0.4 23.125000 36.875000 \n", "5 0.5 23.562500 36.437500 \n", "6 0.6 23.781250 36.218750 \n", "7 0.7 23.890625 36.109375 \n", "8 0.8 23.945312 36.054688 \n", "9 0.9 23.972656 36.027344 \n", "10 1.0 23.986328 36.013672 \n", "11 1.1 23.993164 36.006836 last reaction step" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "c7650ed4-365e-43c2-b001-280297c68ece", "metadata": {}, "source": [ "## NOTE: for demonstration purposes, we're using FIXED time steps... \n", "## Typically, one would use the option for adaptive variable time steps (see experiment `react_2_b`)" ] }, { "cell_type": "markdown", "id": "c034956a-683c-4c3d-8134-ecac9e19a45c", "metadata": {}, "source": [ "### Check the final equilibrium" ] }, { "cell_type": "code", "execution_count": 15, "id": "b139f5e4-625f-4a5e-8f57-8f00244dced4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([23.99316406, 36.00683594])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_system_conc() # The current concentrations, in the order the chemicals were added " ] }, { "cell_type": "markdown", "id": "d25eedf3-89f8-4f8c-a49a-d2689103528b", "metadata": {}, "source": [ "NOTE: Consistent with the 3/2 ratio of forward/reverse rates (and the 1st order of the reactions), the systems settles in the following equilibrium:\n", "\n", "[A] = 23.99316406\n", " \n", "[B] = 36.00683594\n" ] }, { "cell_type": "code", "execution_count": 16, "id": "765f6f39-4b2e-4a86-b6a9-ace9d1941663", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [A] = 23.99 ; [B] = 36.01\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.50071\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 1.5\n", "Discrepancy between the two values: 0.04749 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "905adfdd-6d70-4dfc-bb34-c547c4d604b9", "metadata": {}, "source": [ "### As noted earlier, because of the high initial concentration of B relative to A, the overall reaction has proceeded IN REVERSE" ] }, { "cell_type": "markdown", "id": "6ac3dd4e-9dd0-4d3a-aa83-76102bd79524", "metadata": { "tags": [] }, "source": [ "## Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 17, "id": "86976e6f-f453-41c3-9553-b27b1328db6b", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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Changes in concentrations with time" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 1.0999999999999999 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0005635245901639344, 1.1005635245901637 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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SYSTEM TIMEABcaption
00.010.00000050.000000Initial state
10.117.00000043.000000first reaction step
20.220.50000039.5000002nd reaction step
30.322.25000037.750000
40.423.12500036.875000
50.523.56250036.437500
60.623.78125036.218750
70.723.89062536.109375
80.823.94531236.054688
90.923.97265636.027344
101.023.98632836.013672
111.123.99316436.006836last reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.000000 50.000000 Initial state\n", "1 0.1 17.000000 43.000000 first reaction step\n", "2 0.2 20.500000 39.500000 2nd reaction step\n", "3 0.3 22.250000 37.750000 \n", "4 0.4 23.125000 36.875000 \n", "5 0.5 23.562500 36.437500 \n", "6 0.6 23.781250 36.218750 \n", "7 0.7 23.890625 36.109375 \n", "8 0.8 23.945312 36.054688 \n", "9 0.9 23.972656 36.027344 \n", "10 1.0 23.986328 36.013672 \n", "11 1.1 23.993164 36.006836 last reaction step" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = dynamics.get_history() # Revisited from earlier\n", "df" ] }, { "cell_type": "markdown", "id": "f72f4988-4e4b-4268-9f4a-e36300c9dcf1", "metadata": {}, "source": [ "## Now investigate A_dot, i.e. d[A]/dt" ] }, { "cell_type": "code", "execution_count": 20, "id": "5ee8ec14-442f-4e76-bc86-26b8791f7e70", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[10.0,\n", " 17.0,\n", " 20.5,\n", " 22.25,\n", " 23.125,\n", " 23.5625,\n", " 23.78125,\n", " 23.890625,\n", " 23.9453125,\n", " 23.97265625,\n", " 23.986328125,\n", " 23.9931640625]" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = list(df.A)\n", "A" ] }, { "cell_type": "code", "execution_count": 21, "id": "a390ed46-f014-414f-9b14-69f6da95dc41", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(A)" ] }, { "cell_type": "code", "execution_count": 22, "id": "b3b1b169-bae2-493b-b652-ce9e82b2ddab", "metadata": {}, "outputs": [], "source": [ "A_dot = np.gradient(A, 0.1) # 0.1 is the constant step size" ] }, { "cell_type": "code", "execution_count": 23, "id": "35c7be1f-95ce-4bac-9fb3-02745a505f92", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([7.00000000e+01, 5.25000000e+01, 2.62500000e+01, 1.31250000e+01,\n", " 6.56250000e+00, 3.28125000e+00, 1.64062500e+00, 8.20312500e-01,\n", " 4.10156250e-01, 2.05078125e-01, 1.02539062e-01, 6.83593750e-02])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A_dot" ] }, { "cell_type": "code", "execution_count": 24, "id": "f5fa1f8e-517f-4fd1-b3bf-51c12ab883f0", "metadata": {}, "outputs": [], "source": [ "df['A_dot'] = A_dot # Add a column to the Pandas dataframe" ] }, { "cell_type": "code", "execution_count": 25, "id": "e3773cfc-88ed-4565-a760-e90fa050d5b9", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaptionA_dot
00.010.00000050.000000Initial state70.000000
10.117.00000043.000000first reaction step52.500000
20.220.50000039.5000002nd reaction step26.250000
30.322.25000037.75000013.125000
40.423.12500036.8750006.562500
50.523.56250036.4375003.281250
60.623.78125036.2187501.640625
70.723.89062536.1093750.820312
80.823.94531236.0546880.410156
90.923.97265636.0273440.205078
101.023.98632836.0136720.102539
111.123.99316436.006836last reaction step0.068359
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concentration change per unit time (brown)" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(chemicals=[\"A\", \"A_dot\"], colors=['navy', 'brown'], \n", " ylabel=\"concentration (blue) /
concentration change per unit time (brown)\",\n", " title=\"Concentration of A with time (blue), and its rate of change (brown)\")" ] }, { "cell_type": "markdown", "id": "85d87078-8fc1-4166-95e1-343b546f9971", "metadata": {}, "source": [ "### At t=0 : \n", "[A]=10 and [A] has a high rate of change (70)\n", "### As the system approaches equilibrium : \n", "[A] approaches a value of 24, and its rate of change decays to zero." ] }, { "cell_type": "markdown", "id": "99cd0942-555b-444e-9c6f-ee1481a2a980", "metadata": {}, "source": [ "#### **NOTE:** The curves are jagged because of limitations of numerically estimating derivatives, as well as _the large time steps taken_ (especially in the early times, when there's a lot of change.) \n", "## In experiment \"react_2_b\", we revisit the same reaction using a better simulator that employs _adaptive variable time steps_" ] }, { "cell_type": "code", "execution_count": null, "id": "531ce53b-7336-440e-bce4-716aafa6c692", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }